Question

You are a financial analyst for the Ubuntu Inc. The director of capital budgeting has asked you to analyse two proposed mutually exclusive capital investment projects, projects X and Y. The cost of capital for each project is 1296.The projects, expected net cash flows are as follows 2. Expected Net Cash Flows Project X 0 $100,000 160,500 230,000 3 30,000 4 10,000 Required: 1. Calculate the payback period (0.5 mark) 2. Calculate the discounted payback period, (0.5 mark) 3. Calculate average accounting return, (0.5 mark) 4. Calculate the NPV (1 mark) 5. Calculate IRR (1 mark) 6. Calculate profitability index (0.5 mark)

Answer 1

1. Pay back period = initial investment / divided by cash flows
since the cash flows are uneven here we will deduct one by one.

Initial investment = 100000
Cash flow 1 = 60500
Cash Flow 2 = 30000
now, 90500 is already recovered remaining 9500 will be taken from 3rd year cashflow on pro rata basis
so it should be = 9500/30000 = 0.3167, converting this into months = 0.3167*12 = 3.8
SO the payback period is 2 years and 4months.

2. Discounted pay back period: In this we discount the cashflow as shown below

Year	Cash Flow	PV Factor	PV of cashflows	Cumulative PV
1	60500	0.892857	54017.86	54017.86
2	30000	0.797194	23915.82	77933.67
3	30000	0.71178	21353.41	99287.08
4	10000	0.635518	6355.18	105642.26

As the initial investment of 100000 will be recovered in 4th year, the discount pay back period will be in the 4th Year.

3. average accounting return = average profit/ initial investment
average income = (60500+30000+30000+10000)/4 = 32625
Average accounting return = 32625/100000 = 32.625%

4. NPV at 12%

Year	Cash Flow	PV Factor	PV of cashflows
0	-100000	1	-100000.00
1	60500	0.892857	54017.86
2	30000	0.797194	23915.82
3	30000	0.71178	21353.41
4	10000	0.635518	6355.18
NPV			5642.26

5. IRR is the rate of return which makes the NP zero, it can be calculated using the trial and error method or excel function.
The easier way to calculate it is excel = IRR(Cashflows array, guess)

IRR for this case is = 15.47%

6. Profitability index = PV of inflow/PV of outflow

Year	Cash Flow	PV Factor	PV of cashflows
1	60500	0.892857	54017.86
2	30000	0.797194	23915.82
3	30000	0.71178	21353.41
4	10000	0.635518	6355.18
TOTAL PV			105642.26

PV of Inflow -105642.26
PV of outflow = 100000

PI = 105642.26/100000 = 1.0564